Archive November 2010

Five hundred and seventeen for one. That’s more like it. Looking forward to more of the same in Adelaide.

So, physics. Last week I was doing a bit of work in the lab with a student, trying to track down why his instrumentation wasn’t working. We’re still at it; what he’s trying to do is quite complicated, but we made some progress. One thing we noticed was that there were multiple ground points in the circuit.

What do I mean by this? A lot of electronic equipment is earthed (‘grounded). It’s basically an electrical safety thing. It means that any metal on the outside of the equipment (stuff you can touch) is connected, via the power cable and the earth pin on the plug, to a large piece of metal somewhere outside the building that is hammered well into the ground. What this means is that the outside of the equipment sits at the same electric potential as your feet. If you touch the case with your hand, there is no potential difference between your hand and your feet (which are touching the ground, usually), and so no electric current flows through you. If there’s an electrical fault and the outside case suddenly becomes live, a large current will flow through the earth wire to ground, blowing the fuse.

But a problem can happen if you are using many pieces of electrical equipment as part of an electrical circuit. For example, the negative input to an oscilloscope is often (but not always) connected to ground. When you measure the potential difference in your circuit with such an oscilloscope, the point where you connect the negative terminal becomes ‘grounded’. If you then used a second oscilloscope to monitor another potential difference, you could have two points in your circuit that are forced to a ‘ground’ potential.

That doesn’t work. What happens is that you have introduced a short-circuit between the two ground points. In effect, you’ve connected a wire between them. However, the ‘wire’ is slightly obscure – it journeys from the negative input of the first oscilloscope, down the earth wire of the power cord, where it probably joins somewhere with the earth wire of the power cord from the second oscilloscope, then it goes up that earth wire and to the negative terminal of the second oscilloscope. There could be a substantial current flowing around this loop. What it will do to your circuit will depend on what the circuit is, but for sure it will mean that the circuit won’t do what you want it to.

Usually, with a spot of thinking, you can reorganize what you’re plugging in to the circuit to measure it so that you avoid the problem.

The moral – you can only have one earth point on a circuit. Watch what you plug in to monitor the circuit – it may be earthed.

What a dismal and predictable start to the Ashes. Turn your back on the computer screen for five minutes and suddenly England have lost three wickets.

Anyway, yesterday I was in Auckland, talking about research progress with a group that we’ve had strong links with in the past. (By ‘we’ I mean the Waikato cortical modelling group). One of the talks we heard was a very enthusiastic affair on re-invigourating analogue computing.

The word ‘analogue’ has relatively recently come to mean ‘not digital’ but we were reminded of just where the use came from. An analogue computer is an electrical analogue of another system. For example, we can create an electrical system whose underlying physics is entirely analogous to a physical system (e.g. a mechanical system) that we wish to study. Therefore, building the electrical system and seeing how its voltages change with time will tell us exactly how the mechanical system will change with time. So we have ‘solved’ the behaviour of a mechanical system just by building an electrical circuit.

The operational amplifier allows us to make small circuit elements that add, take logs, and, very importantly, integrate or differentiate. This means we can put these elements together to make a system that obeys a set of differential equations. For example, if you wish to study the trajectory of a projectile in three dimensions (with air resistance) you can write the underlying physics in six coupled first-order differential equations (two for each of the x, y and z components). You can then make up a circuit with six operational-amplifiers whose voltages obey the same equations. If you want to change, say, the coefficient of air resistance, we can do this by changing a few resistor values.

Let the circuit run, and, hey-presto, you have the solution to your problem. There is a degree of elegance here that is lost with a digital interpretation of the same problem. In the digital method, we would have to break down the problem into a series of small time steps, and ask ourselves the question – if my system is in state X now, what state will it be in at a small time in the future? Then, knowing what state it is in a small time in the future, we can ask the same question again – what state will it be in at another small step into the future? And so forth.

Of course, the real world doesn’t work in discrete time steps, but we have to introduce them to get a digital computation to work. We then try to balance accuracy with run-time – to get the most accurate solution we need small time steps, but if you have small time steps you need more of them, which takes longer to compute. In the analogue method there is no such problem. Your circuit just does its stuff in continuous time, just like a real system. Much more elegant.

Alison has drawn my attention to this video showing a cat lapping milk in slow motion. The professor explains that the cat doesn’t scoop up the liquid like a dog would, but uses the tip of its tongue – the liquid adheres to the tongue and is drawn up in a thin column. The cat is making use of some sophisticated fluid mechanics to drink.

It’s a very clean way of transferring liquid from the bowl to the mouth, rather fitting for a creature whose fourth most important activity is cleaning itself (the other three more important activities being sleeping, eating, and staring out of the window). A whole lot less messy than a dog. However, it also looks a whole lot less efficient.

A rather fun result, but I don’t think its a new finding. There are plenty of online videos showing exactly the same thing.

I got home from work last night to discover the decorator still hard at work, putting up the ‘feature’ wallpaper on one fairly small section of wall. He said he’d been struggling for the last hour trying to find the repeat in the pattern. It’s a dark paper, with detailed but low-contrast outlines of flowers in it. Being an expert in this, having done first-year crystallography, I looked at it very carefully. Little wonder the poor guy was struggling. The label on the roll said it repeated every 32 cm. It didn’t. It nearly repeated every 32 cm, but there were some subtle differences. The repeat length was actually 64 cm. Once we’d got this sorted, the rest was fairly easy. In crystollagraphic language, we have a rectangular lattice, with lattice constant 64 cm vertically and about 50 cm horizontally (the width of the roll). The motif has no symmetry at all – i.e. the end result simply has translational symmetry. That’s a p1 wallpaper group.

There is new wallpaper going up in our house. Since my DIY skills are marginally better than my cat’s, we’ve employed a decorator to do it. (I fixed a dripping tap once – that was the high point of my DIY activity.)

Looking at the new wallpaper has reminded me that I studied it in my first year at university, as part of my ‘Crystalline Materials’ course. What has wallpaper got to do with crystalline materials? It’s a good example of lattices and symmetry.

Wallpaper, unless it is completely bland, contains repeating patterns. Have a look at some and see if you can identify exactly what the nature of the pattern is. You can describe it by a ‘lattice’ and a ‘motif’. The lattice is a set of equivalent points on the pattern. Imagine doing the following (or do it for real if you are about to strip the wallpaper). Look at your wallpaper, pick a point on it, put a nice big dot with a marker pen on that point. Then go and find all the other points on the wallpaper that are at the exact same point in the pattern as this one, and put a dot there too. Sometimes you have to think carefully about whether two points really are equivalent. The key is that if you picked up the whole sheet of wallpaper and moved it so that one dot landed on another dot (no rotating allowed) the final result on your wall would be unchanged. What you are left with is a lattice of dots on your wallpaper.

On wallpaper, which is two dimensional, there are only five distinct symmetries the lattice can have. An obvious one is ‘square’ symmetry – your dots will form a square lattice. But there are others – hexagonal, rectangular, centred-rectangular and oblique.

In three dimensions, which is the domain of crystals, there are fourteen distince lattices.

Connected with the lattice, is the motif. This describes the pattern itself. If we take a motif, and apply it at every lattice point, we reconstruct the whole wallpaper.

Then, there are the symmetries. These are obviously related to the lattice, but are not the same thing. Think about the ways that you can reflect, rotate and translate the wallpaper so that the pattern remains unchanged. (A translation from one lattice point to another by definition does this). There are seventeen different symmetries a wallpaper can have. Which is yours? In three dimensions, there are 32 different crystal symmetries, which are very important in crystallography. These are called the crystallographic point groups.

After studying crystallography, even for a short while, you’ll never look at wallpaper the same way again.

This week I’ve had three fairly lively discussions about learning outcomes in our university papers. (It’s well blogged already – e.g. here, but I’ll add some things to the mix). The concept is hardly new, but it is only just being given a really wide profile here at Waikato. Although many individual teachers, and many departments, have routinely written learning outcomes for their papers up to this point, it is now becoming mandatory. This is causing a bit of anxiety.

I honestly think that most of the adverse reaction is because it is seen as being another piece of administration work to do that has nothing to do with the task of actually teaching. In fact, it has everything to do with the task of teaching. Simply put, if you don’t know what the learning outcomes for your paper are, your teaching really has no purpose.

I was having a conversation last week with a student about negative resistances (in an electronics context). These are just as they sound – to send a current from terminal A to terminal B you have to apply a higher potential to terminal B than terminal A. Sounds backwards? Yes – it is. That’s why the resistance is negative.

It’s not possible to get a negative resistance with purely passive components. We can see that from thermodynamics. A normal (positive) resistor puts out heat to the surroundings – voltage times current gives us the power dissipated. A negative resistor would need to suck in heat and turn it to electrical energy. For example, if you connected a negative resistor to a battery, the current would flow backwards through the battery – i.e. charge it up. The energy would come from the surroundings, being sucked in by the negative resistor. It would be a nice solution to global warming, but unfortunately the second law of thermodynamics says you can’t do it.

So how can you get a negative resistance? You can use active components – e.g. operational amplifiers, that have a power source. There are a few circuits that effectively produce a negative resistance, for example this one. To put a positive current into the circuit, you have to apply a negative potential difference. If I put a battery across the terminals, it would recharge. Where does the energy come from, if it can’t come from the surroundings? The operational amplifier needs its own power supply – that is, it is not a passive component. The second law of thermodynamics can rest easy.

There are lots of neat applications – perhaps the most obvious is simply ’cancelling’ unwanted positive resistances. Related to negative resistance, but not the same thing, is negative differential resistance. This is something that can be made from a purely passive component, for example in a tunnel diode. Here, if you plot a graph of the current through the diode (y-axis) against the voltage across the diode (x-axis) there is a region where the gradient is negative. That is, increasing the voltage causes less current to flow. However, this doesn’t break the second law of thermodynamics since the current is still positive for a positive voltage. In calculus terms, dV/dI is negative (in a small region), though V/I remains positive. Tunnel diodes can be used in oscillators.

There are lots of cool things you can do with Operational Amplifiers, negative resistances are just one. Have a go at making a negative resistance, and see what you can do with it.

It’s an old (1997) report on ‘electronic’ pest control devices. On ‘electromagnetic’ devices, it comments "Laboratory efficacy tests on the control of Norway rats … indicated definitively that such devices have no effect on feeding, drinking, mating or infestation patterns." Hmmm.It goes on to report of legal action being taken in the US against sellers of such devices.Also curious, is that when I look at devices on sale, electromagnetic is always combined with ultrasonic. This leads me to suspect that it is the ultrasonic bit that works, and the electromagnetic bit does absolutely nothing in way of deterring your rodent pests.But I’m open to be corrected, if anyone can point me to some science.

I saw in the newspaper yesterday an advert for an ‘ultrasonic and electromagnetic’ mouse and rat repeller. That got me interested. The ultrasonic bit seems to be plausible enough – I don’t know much about rodent ear physiology, but I’m willing to believe they can hear sounds at higher frequency to us and to dogs and cats (which, the advert claims, are unaffected.) It’s the electromagnetic bit that has me interested.

Cables to carry electromagnetic signals? That’s perfectly reasonable – an electrical signal on your house supply is how your electricity company can switch power on and off to your hot water cylinder remotely, for one thing. But what sort of signal, and what does it do to our rodent friends, and, moreover, why doesn’t it do the same to us?

So we are on ‘aggravating the nervous system now’. A quick search on ISI Web of Science for journal articles on spider, nervous system and electromagnetic waves is giving me nothing. But what I do know is that there have been lots of studies on things like cell phones and people, which show that there isn’t much effect of EM waves on people (unless you get up to X-rays and gamma-rays), so I’m wondering why it would be different for other animals.

Anyway, to summarize, I’m intrigued. Does any one have ideas as to what these machines are 1. actually doing with your household wiring, and 2. what is the effect on the mouse / rat, and 3. why don’t we and cats / dogs respond in the same manner? (Remember, it’s the electromagnetic bit I’m puzzled by, not the ultrasonic.)

The warm sunny weather has led to a discovery under the front lawn. The clue was the fact that the ground was squelchy after three weeks with no rain. Either a new hot spring was in the process of popping up out of the lawn, or our water pipe had sprung a leak.

It’s not the first time (or even the second time) that it’s had a leak. The plumber says that the problem is that the pipe (a plastic one) isn’t tough enough for the high Cambridge water pressure. True, he might be fishing for a contract to replace the whole pipe, but with three leaks in the last few years (and how many more before we moved into the house, I don’t know) he probably has a point.

This has reminded me about a bit of theory I did back as an undergraduate on how the pressure of the water in a pipe relates to the stress in the wall of the pipe. It’s a relatively simple calculation to do – if you consider the top half of a section of pipe, you can balance the force upward on the pipe due to the water pressure with the force downward due to the stress in the pipe wall.

We find that the stress (tension force per unit area) is proportional to the pressure (unsurprisingly) multiplied by the pipe radius but divided by its thickness. That is, a thin pipe (by which I mean a pipe with a thin wall, not one with small diameter) is under a greater stress than a thick one. What the pipe is made of doesn’t influence the stress it is under, but it will influence the breaking stress.

So, to get a more suitable pipe, it either needs to have a thicker wall (and therefore less flexible), or made from a material with higher breaking stress. (Or of smaller radius, which constricts water flow, so that’s not necessarily an option.) Which, I’m not fussed, just so long as it doesn’t break again! Fed up with digging holes in the lawn.

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